The present invention relates to a fuzzy logic controller of the analog type which implements a set of fuzzy rules with which are respectively associated output values which can be expressed as as many polynomials of a same set of input variables, the coefficients of said polynomials having predetermined values (possibly equal to zero) specific to the different rules and each of said rules including at least one condition consisting of a fuzzy relationship between one of said input variables and a reference value.
Known fuzzy logic controllers are provided in order to implement fuzzy rules for which the output values are predetermined constants. Such fuzzy rules define an association between a fuzzy subset of an input space and a point in an output space. Typically, such a known fuzzy rule will take the following form: EQU IF x.sub.1 .apprxeq.p.sub.1 AND x.sub.2 .apprxeq.p.sub.2 THEN y=u
where p.sub.1 and p.sub.2 are reference values which define the center of a fuzzy domain or subset and in which u is a predetermined constant quantity (scalar or possibly vectorial) which defines a point in an output space of any dimension.
Since a fuzzy rule defines, as we have just mentioned, an association between a domain of an input space and a point of an output space, a set of such rules enables defining region by region a relationship between variables in the input space and variables in the output space.
When the domains of the input space associated with the different rules are disjunctive the relationship defined by the set of rules causes each domain to correspond simply with the corresponding points of the output space. On the other hand, when the domains of the input space associated with the different rules overlap one another, it is necessary to provide an algorithm in order to permit determination in unequivocal fashion of an unique global output magnitude for the set of rules in the overlapping zones of the domains.
The algorithm most frequently used in order to determine a global output value for a set of rules is the calculation of the center of gravity. Such center of gravity calculation comes down to the calculation of a weighted average of the output magnitudes of the different rules, the weighting factor being the weight (or degree of pertinence) of each of such rules. Let us point out nevertheless that other algorithms have been proposed in order to fulfil the same function and that all such algorithms are generally known as "defuzzification" algorithms.
The output magnitudes of the fuzzy rules of the type of those described hereinabove being constant, the slope of the relationship binding the input and output magnitudes is not explicitly defined by the rules themselves, but follows from the algorithm for combining the conclusions of the rules in the overlapping zones.
In certain applications of fuzzy logic, the exact manner according to which the global output value of the set of rules varies, can be important in certain regions. A slightly more general formulation of the idea of fuzzy rules has thus been proposed, in particular by T. Terano, K. Asai and M. Sugeno in the work "Fuzzy Systems Theory And Its Application", Academic Press 1992. According to this new formulation, the output values of fuzzy rules are no longer forcibly constant magnitudes, but can also be functions of the input values. Such a rule is expressed then for example by: EQU IF x.sub.1 .apprxeq.p.sub.1 AND x.sub.2 .apprxeq.p.sub.2 THEN y=g(x.sub.1, x.sub.2)
The present invention more specifically concerns fuzzy rules the output values of which can be expressed as polynomial functions.
In order to evaluate a global output value of a set of fuzzy rules for which the respective output values can be expressed as polynomial functions of the input variables, the standard procedure will be applied as follows:
initially, for each of the rules, the associated polynomial function is evaluated, as well as the weight or degree of pertinence of said rule;
next, starting with the different output values and taking into account the weight of each rule, there will be calculated the global output value of the set of rules in applying a "defuzzification" algorithm.
As can be appreciated, the manner of proceeding set forth hereinabove requires estimating the value of a different polynomial for each rule. In the case of implementing the procedure with the help of an analog device, an electronic circuit intended to evaluate a polynomial must be provided for each rule of the set of rules. The implementing of the process which has just been described with the help of analog circuits thus exhibits the drawback of being expensive in hardware.